First slide

Vectors

Question

In the figure shown, ABCDEF is a regular hexagon. What is the value of AB + AC + AD + AE + AF?

Moderate

A

AO
B

2AO
C

4AO
D

6AO

Solution

AB+ AC+ AD+ AE+ AF
$= AB + (AB + BC) + (AB + BC + CD) + (AB + BC + CD + DE) + AF$
$= 4 AB + 3 BC + 2 CD + DE + AF$
$(∵ AB = - DE, BC = - EF, AF = CD)$
$= 3 (AB + BC + CD) = 3 AD = 6 AO$

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